Question #6453330Fill in the Blank
Algebra-1
Question
The end behavior of the polynomial as is ______ and as is ________.
Answer & Analysis
Analysis
Question Analysis
This question assesses the student's ability to determine the end behavior of a polynomial function based on the leading term and its coefficient.
This question assesses the student's ability to determine the end behavior of a polynomial function based on the leading term and its coefficient.
Key Concept Explanation
The end behavior of a polynomial is governed by the leading term, which is the term with the highest degree. For odd degrees, the ends of the graph will go in opposite directions depending on the sign of the leading coefficient.
The end behavior of a polynomial is governed by the leading term, which is the term with the highest degree. For odd degrees, the ends of the graph will go in opposite directions depending on the sign of the leading coefficient.
Step-by-step Solution
1. Identify the leading term:
2. Determine the degree: 3 (odd)
3. Determine the leading coefficient: -2 (negative)
4. Apply the end behavior rules for odd degrees and negative leading coefficients:
As ,
1. Identify the leading term:
2. Determine the degree: 3 (odd)
3. Determine the leading coefficient: -2 (negative)
4. Apply the end behavior rules for odd degrees and negative leading coefficients:
As ,
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